Advective accretion flow around a black hole is likely to have two saddle-type sonic points. After the accretion flow with the appropriate injection parameters passes through the outer sonic points, the supersonic flow can be virtually stopped by the centrifugal force, forming a standing shock close to the black hole and again falling into the black hole supersonically. Apart from general researches on the shock wave, the study of the standing shock in the accretion disc flow under an astrophysical context was pioneered by
[1]}. He examined the transonic disc accretion onto a black hole with a fully relativistic treatment, assuming constant disc height and found multiple critical points as well as a transition through standing shock. [2]} considered the hydrostatic equilibrium in the vertical direction and presented analytically the transonic solutions which include the standing shock in the rotating adiabatic flow under the pseudo-Newtonian potential of the black hole.
Further studies of the standing shocks in the low angular momentum flows have been developed
for parameter space research of the specific internal energy \(\mathcal {E}\) 
and the specific angular momentum \(\lambda \)  responsible for the standing shock [3]}, [4]}, [5]}, for 2D numerical simulations of the shocks by smoothed particle hydrodynamics (SPH) or Eulerian 2D hydrodynamics [6]}, [7]}, [8]}, [9]}, [10]}, for astrophysical applications such as hard X-ray emission from the post-shock region, mass outflow rate and quasi-periodic oscillations (QPOs) phenomena [11]}, [12]}, [13]}, [14]} and for effects of cooling, viscosity, and magnetic field on the standing shock [15]}, [16]}, [17]}, [18]}, [19]}.
However, there are only several 1D theoretical [20]}, [21]}, [22]}, [23]} and 2D numerical studies [24]}, [25]} of radiative standing shock, where the radiation influences on the shock structure of the pre-shock and the post-shock regions.
